Non-Abelian topological phases in an extended Hubbard model

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We describe four closely related Hubbard-like models (models A, B, C and D) of particles that can hop on a 2D Kagome lattice interacting via Coulomb repulsion. The particles can be either bosons (models A and B) or (spinless) fermions (models C and D). Models A and C also include a ring exchange term. In all four cases we solve equations in the model parameters to arrive at an exactly soluble point whose ground state manifold is the extensively degenerate ``d-isotopy space'' Vd, 0<d<2. Near the ``special'' values, d = 2 π/k+2, Vd should collapse to a stable topological phase with anyonic excitations closely related to SU(2) Chern-Simons theory at level k. We mention simplified models A- and C- which may also lead to these topological phases.